Circular Geodesics in Tidal Charged Black Hole

TL;DR

This paper analyzes the geodesic structure and stability of circular orbits in tidal charged black holes, comparing them with Reissner-Nordström black holes, and explores their potential as particle accelerators.

Contribution

It provides a detailed comparison of geodesic structures, derives key orbital parameters, and calculates quasi-normal modes for tidal charged black holes, highlighting their unique properties.

Findings

Comparison of geodesic structures between tidal charged and Reissner-Nordström black holes.

Derivation of ISCO, MBCO, and CPO for both spacetimes.

Tidal charged black holes can act as particle accelerators with ultra-high energy near the horizon.

Abstract

We study the existence and stability criteria for circular geodesics of spherically symmetric tidal charged black hole~(BH). We investigate in details the equatorial causal geodesics of the tidal charged BH in comparison with spherically symmetric Reissner-Nordstr\"{o}m BH spacetime. We particularly focused on both the null circular geodesics and time-like circular geodesics. Using the effective potential diagram, we have compared the geodesic structure between two spacetimes. We have derived the ISCO~(innermost stable circular orbit), MBCO~(marginally bound circular orbit) and CPO~(circular photon orbit) for both the space-times. Moreover, we have derived the \emph{quasi-normal modes~(QNM) frequency} in the \emph{eikonal limit} for both the spacetimes via Lyapunov exponent. In the Appendix section, we have shown that a spherically symmetric tidal-charged BH can act as particle accelerators with ultra-high center-of-mass~(CM) energy in the limiting case of \emph{maximal BH tidal charge~($q$)} and it is possible when two neutral particles are colliding near the horizon.